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#include <bits/stdc++.h>

using namespace std;

int n;
string s;

vector<int> getSkrajne() {
  vector<int> skrajne;
  if (s[0] == '0') {
    int cnt = 0;
    while (cnt + 1 < n && s[cnt + 1] == '0') {
      cnt++;
    }
    ++cnt;
    skrajne.push_back(cnt);
  }
  if (s[n - 1] == '0') {
    int cnt = s.size() - 1;
    while (cnt - 1 >= 0 && s[cnt - 1] == '0') {
      cnt--;
    }
    cnt = s.size() - cnt;
    skrajne.push_back(cnt);
  }
  return skrajne;
}

void solve() {
  cin >> n;
  cin >> s;

  vector<int> skrajne = getSkrajne();
  if (skrajne.size() > 0 && skrajne[0] == n) {
    cout << 0 << endl;
    return;
  }
  sort(skrajne.begin(), skrajne.end());

  int first1 = n;
  int last1 = 0;
  for (int i = 0; i < n; ++i) {
    if (s[i] == '1') {
      first1 = min(first1, i);
      last1 = max(last1, i);
    }
  }

  vector<int> seg;
  for (int i = first1; i <= last1; ++i) {
    if (s[i] == '1') {
      while (i < n && s[i] == '1') {
        ++i;
      }
      --i;
      continue;
    }

    int first0 = i;
    while (i < n && s[i] == '0') {
      ++i;
    }
    seg.push_back(i - first0);
  }
  sort(seg.begin(), seg.end());

  int res = 0;
  int day = 0;
  while (!seg.empty() || !skrajne.empty()) {
    int bestSeg = -1;
    if (!seg.empty()) {
      bestSeg = max(seg.back() - 2 * day - 1, 0);
      if (seg.back() - 2 * day == 1) {
        bestSeg = 1;
      }
    }

    int bestSkrajny = -1;
    if (!skrajne.empty()) {
      bestSkrajny = max(skrajne.back() - day, 0);
    }

    bool skrajne2 = false;
    if (skrajne.size() == 2) {
      int summ = skrajne[1] - day + max(0, skrajne[0] - day - 1);
      if (summ > bestSeg) {
        bestSeg = summ;
        skrajne2 = true;
      }
    }

    // cout << bestSeg << " " << bestSkrajny << " " << seg.size() << " " << skrajne2 << endl;
    if (bestSeg == 0 && bestSkrajny == 0) {
      break;
    }
    if (bestSeg == -1) {
      skrajne.pop_back();
      res += bestSkrajny;
      ++day;
      continue;
    }
    if (bestSkrajny == -1) {
      seg.pop_back();
      res += bestSeg;
      if (bestSeg <= 0) {
        break;
      }
      day += min(2, bestSeg);
      continue;
    }


    if (bestSeg > bestSkrajny) {
      if (skrajne2) {
        res += skrajne.back() - day;
        skrajne.pop_back();
        day += 1;
      } else {
        seg.pop_back();
        res += bestSeg;
        day += min(2, bestSeg);
      }
      if (bestSeg <= 0) {
        break;
      }
    } else {
      skrajne.pop_back();
      res += bestSkrajny;
      day++;
    }
  }
  cout << n - res << endl;
}

int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);  
  int t;
  cin >> t;
  while (t--) {
    solve();
  }
}